(2-1), must be
(2-36)
This force is delivered by the motor in the form of a torque T, which is related to f, using Eq. (2-35), as
(2-37)
Therefore, the electromagnetic torque required from the motor is
(2-38)
In the vehicle of Example 2-6 with Cw = 0.5, assume that each wheel is powered by its own electric motor that is directly coupled to it. If the wheel diameter is 60 cm, calculate the torque and the power required from each motor to overcome the drag force when the vehicle is traveling at a speed of 100 km/h.
Solution
In Example 2-6, the vehicle with Cw = 0.5 presented a drag force fL = 413.7 N at the speed u = 100 km/h. The force required from each of the four motors is
From Eq. (2-35),
Therefore, the power required from each motor is
2‐7‐2 Gears
For matching speeds, Fig. 2-15 shows a gear mechanism where the shafts are assumed to be of infinite stiffness, and the masses of the gears are ignored. We will further assume that there is no power loss in the gears. Both gears must have the same linear speed at the point of contact. Therefore, their angular speeds are related by their respective radii r1 and r2 such that
and
Combining Eqs. (2-39) and (2-40),
where T1 and T2 are the torques at the ends of the gear mechanism, as shown in Fig. 2-15. Expressing T1 and T2 in terms of Tem and TL in Eq. (2-41),
From Eq. (2-42), the electromagnetic torque required from the motor is
where the equivalent inertia at the motor side is
Fig. 2-15 Gear mechanism for coupling the motor to the load.
Optimum Gear Ratio
Equation (2-43) shows that the electromagnetic torque required from the motor to accelerate a motor‐load combination depends on the gear ratio. In a basically inertial load where TL can be assumed to be negligible, Tem can be minimized, for a given load‐acceleration
(2-45a)
and, consequently,
(2-45b)
With the optimum gear ratio, in Eq. (2-43), using TL = 0, and using Eq. (2-41),
(2-46)
Similar calculations can be made for other types of coupling mechanisms (see homework problems).
2‐8 TYPES OF LOADS
Load torques normally act to oppose rotation. In practice, loads can be classified into the following categories [2]:
1 Centrifugal (Squared) Torque
2 Constant Torque
